CH302: Unit 4 Exam Review
Fundamentals of Nuclear,
Kinetics
Common Mistakes
• Myths we told you, and why they’re not true:
– Myth: Stoichiometry doesn’t matter in kinetics
• Stoichiometry is essential for determining the rate order of
elementary steps
• Stoichiometry is essential for determining “relative rates” of
reactions
• Stoichiometry does not necessarily indicate anything about the
rate given the overall balanced reaction (this should be obvious
now that we know all about mechanisms)
– Myth: The order of a reaction or reactants are whole
number integers
• When using the method of initial rates, empirically derived rate
orders can be any value (fractions included)
• In CH204L, we rounded the rate order – in reality, we do not
round the empirical rate order
• You can end up with fractional rate orders when you take a
square root in kinetic equilibrium problems or when solving for
the rate using the method of initial rate
Kinetics
Exam 4 Learning Objectives
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Complete nuclear reactions with a given unknown (identify the missing decay particle or product)
Define nuclear particles: associated atomic number, mass, and charge
Understand how the “band of stability” can predict decay events
Calculate the change in energy or mass associated with a nuclear reaction
Define and differentiate fusion and fission
Calculate the rate of consumption and production given the overall balanced chemical reaction
Rate law concepts: understand the attributes of a rate law including the definition of rate order, rate
constant, dependence on concentration, and the units involved
Empirical rate law: use the method of initial rates to determine the rate order or unknown
concentrations of a given reaction
Empirical rate law: know the definition and application of pseudo-first order reactions
Integrated rate laws: use the integrated rate laws to determine the value of k or concentration at a given
time
Integrated rate laws: use the integrated rate laws to determine solve problems using half-life given
information about the order
Apply the rate law equations to graphs given information about the order of the reaction
Understand that there are four main factors that affect rates
Understand how temperature affects the rate
Understand the main role and properties of a catalyst
Arrhenius law: Solve for new temperatures using a change in the rate constant (k) or vice versa
Apply Arrhenius law to graphs relating activation energy and temperature to the rate constant
Use the elementary step of a reaction mechanism to determine the rate law
Apply the ideas of kinetic equilibrium to solve for the rate law of a provided mechanism
Identify the intermediates and reactants/products of a reaction mechanism
Identify the data associated with reaction coordinate diagrams
Understand the attributes of transition state theory
Nuclear Learning Objectives
• Complete nuclear reactions with a given unknown (identify the
missing decay particle or product)
• Define nuclear particles: associated atomic number, mass, and
charge
• Understand how the “band of stability” can predict decay events
• Calculate the change in energy or mass associated with a nuclear
reaction
• Define and differentiate fusion and fission
Nuclear Chemistry Basics
• You should be aware of the 4 main types of nuclear decay:
– α decay: emission of an α-particle
• The result is a new atomic species (z-2, m-4) and a new mass
• Note: an alpha particle is a charged helium ion because it has 0 electrons.
A chemist would write it as He2+
– β decay: emission of an electron
• The result is a new atomic species (z+1) with the same mass
– β+ decay: emission of a positron
• The result is a new atomic species (z-1) with the same mass
– Electron capture: the addition of an electron
• The result is a new atomic species (z-1) with the same mass
– Neutrons are also common byproducts/reactants of nuclear
reactions
• The affect of neutron release (m-1) or absorption (m+1) is a change in
atomic mass without a change in a change in z
• Neutrons often pair with other reactions (fusion or fission, for example),
so there are other changes going on to the nuclei
Define nuclear particles: associated atomic number, mass, and charge
Nuclear Chemistry Basics
• It is worth mentioning that these are very
simple to visualize as chemical reactions,
as shown below:
• Alpha decay:
• Beta decay:
• Beta+ decay:
• Electron capture:
Complete nuclear reactions with a given unknown (identify the missing decay particle or
product)
The Band of Stability
• The Band of Stability is a
tool that shows how stable
nuclei favor an ideal
neutron : proton ratio
• This ratio begins as 1:1, but
eventually favors a higher
ratio (more neutrons)
• You can determine the
most likely form of nuclear
decay based on the
relationship between a
selected atom and the band
of stability.
Understand how the “band of stability” can predict decay events
The Energy of a Nuclear Reaction
• Nuclear reaction produce massive amounts of energy
by harnessing the short-wavelength energy potential
of matter
• The energy of a nuclear reaction can be quantified
through the well-known equation:
E = mc2
• Energy is expressed in units of joules, meaning your
mass has to be kg and your speed of light is
meters/second (don’t forget to square c)
– Note: these problems can be made far more difficult if we
include small scale nuclear reactions (ex: mass defect,
binding energy, etc.) – In these cases, you may need to use
more complicated units to solve for energy or mass.
Calculate the change in energy or mass associated with a nuclear reaction
Fusion vs. Fission
• Fission: the splitting or large nuclei into medium size nuclei
– The products of fission are often nuclei larger than iron
(anything that is smaller than iron would be an endothermic
reaction)
– Decay is not a form of fission because the released products are
far too small
• Fusion: the merging of two small nuclei into a larger nuclei
– Fusion typically involves small nuclei, such as hydrogen,
deuterium, and helium. However, fusion is technically an
exothermic process up until iron.
– Similar to my point on fission, beta or alpha capture is not fusion
• In summation:
– Fission can be spotted by the splitting of large atoms
– Fusion can be spotted by the merging of small atoms
Define and differentiate fusion and fission
Kinetics
Quantifying Rates Learning Objectives
•
•
•
•
•
•
•
Calculate the rate of consumption and production given the overall
balanced chemical reaction
Rate law concepts: understand the attributes of a rate law including the
definition of rate order, rate constant, dependence on concentration,
and the units involved
Empirical rate law: use the method of initial rates to determine the rate
order or unknown concentrations of a given reaction
Empirical rate law: know the definition and application of pseudo-first
order reactions
Integrated rate laws: use the integrated rate laws to determine the value
of k or concentration at a given time
Integrated rate laws: use the integrated rate laws to determine solve
problems using half-life given information about the order
Apply the rate law equations to graphs given information about the
order of the reaction
The Relative Rate of a Reaction
• Definition: The relative rate of a reaction refers to the rate of
production per mole reaction (units: M/S)
• It should be easy to see that this rate is stoichiometry
dependent
– For example: the rate of production of a product with a
coefficient of 2 will be twice as fast as the rate of production of a
product with a coefficient of 1
– Common question: why do we divide by the coefficient if the rate
is increasing (the answer can be understood conceptually, but it
is easiest to plug in values and see how it works)
• You can solve for the relative rate of a reaction at any given
time provided that you have a graph
Calculate the rate of consumption and production given the overall balanced chemical reaction
The Relative Rate of a Reaction
• You can solve for the relative rate of a reaction at any given
time provided that you have a graph
– The rate of a reaction at any given time is equal to the slope of
the line tangent to your point in time
This image depicts the
rate (d[H2O2]/dt) at t =
10hrs
Apply the rate law equations to graphs
The Rate Law of a reaction
rate = k[A]x[B]y
•
•
•
This is the most common format to express a rate.
The rate law is often determined experimentally.
The exponents x,y can be any value except 0 (including
fractional values)
–
•
Note: the exponents can technically be equal to 0, but if they
are, we remove that term from the rate law
The order of the reactants is based on the exponents; the
order of the overall reaction is the sum of exponents
– Our units of k are dependent on the order of the total reaction:
•
•
•
•
0th order: k = Ms-1
1st order: k = s-1
2nd order: k = M-1s-1
3rd order: k = M-2 s-1
Rate law concepts: understand the attributes of a rate law including the definition of rate order,
rate constant, dependence on concentration, and the units involved
What Does Order Mean?
• In chemical kinetics, the order of a reactant is the power to
which a reaction depends on the concentration of that
particular reactant.
• Let’s look at A in our generic reaction: 2A + 3B -> 2C + 3D, where
our rate = k[A]x[B]y
– 0th order: the reaction does not depend on the reactant
• X = 0, our [A]x term is equal to 1
• Multiply [A] by 2, you have no change in rate
– 1st order: the reaction depends on the reactant linearly
• X = 1, the rate is proportional to any change in [A]
• Multiply [A] by 2, your rate multiplies by 2
– 2nd order: the reaction depends on the reactant squared
• X = 2, the rate is proportional to any change in [A]2
• Multiply [A] by 2, your rate multiplies by 4
Rate law concepts: understand the attributes of a rate law including the definition of rate order,
rate constant, dependence on concentration, and the units involved
Methods of Initial Rates
• The following reaction is the bromination of pentene:
C5H10 + HBr -> C5H11Br
• The rate is written as rate = k[C5H10]x[HBr]y. Use the
following data to solve for x, y, and k:
Trial #
[C5H10]
[HBr]
Rate
1
2M
2M
10M/s
2
4M
2M
20M/s
3
4M
4M
40M/s
Be familiar with the equation:
***There
are a few
questions
on this
topic, so
please
know it!***
This
equation
can be
expanded
for more
than 2
reactants!
Empirical rate law: use the method of initial rates to determine the rate order or unknown
concentrations of a given reaction
Methods of Initial Rates
Trial #
[C5H10]
[HBr]
Rate
1
2M
2M
10M/s
2
4M
2M
20M/s
3
4M
4M
40M/s
What are you doing here:
• You are measuring the initial rate of a reaction to determine the
dependence of the rate on the concentration of your reactants
• This experimental technique can be applied to reactions with more
than two reactants, and sometimes there is not a clear way to cancel
out all your terms – trust your equation if you get stuck
• Rate orders do not have to be whole number integers
• Eventually you can solve for x, y, and k using the equation:
• Rate = k[C5H10]x[HBr]y
Solution
Trial #
[C5H10]
[HBr]
Rate
1
2M
2M
10M/s
2
4M
2M
20M/s
3
4M
4M
40M/s
• Between trials 1, 2: we doubled the concentration of pentene and the
rate doubled. No change was made to bromine.
• Between trials 2, 3: we doubled the concentration of bromine and
the rate doubled. No change was made in pentene. This is indicative
of a reaction that is first order in bromine.
• Now that we know the order of the reaction, we can set up our
equation: rate = k[C5H10]1[Br2]1. The reaction is second order overall.
• We can use any trial to solve for k. For example: 10M/s =
k(2M)(2M), k = (10M/s )/ (2M)2, k = 2.5M-1S-1
• Important: trials 1, 3 don’t make for a great comparison at the
beginning because both reagents have different concentrations. It’s
difficult to determine which reagent is causing the rate to change
Pseudo-First Order: Definition, Application
Suppose: rate = k[A][B]
•
It is much easier to calculate the rate of a first order reaction
than a second (or higher) order reaction
We can therefore design an experiment where one of our
reactants remains relatively unchanged. We do this by
making the concentration of B way larger than A
In other words, the order of [B] virtually becomes 0 for any
experiment we run with these concentrations
This changes our rate to a first order expression:
–
–
–
–
New rate law: rate = k’[A]; where k’ = k[B]
We can use the data we get from a pseudo-first order
experiment to determine the rate constant of the
corresponding second order reaction
–
•
•
What does this mean? If we set up an experiment to determine k’, we
can get back to k simply by dividing out the concentration of the high
concentration
k = k’/[B]
Empirical rate law: know the definition and application of pseudo-first order reactions
The Integrated Rate Law of a reaction
(Integrated Rate
Law for first order)
•
Rate laws are great for determining the initial rate, but they are
unable to directly predict the rate or concentration of a
product/reactant at any given time in the future (or in the past)
–
•
The integrated rate law solves this by directly measuring
concentration at any given time
Integrated rate law questions can be easily identified because they
generally ask for or provide 1) initial and final conditions and/or 2)
an amount of time that has elapsed. Also, notice how the rate is
nowhere in the equation (this is because the rate is changing for
every second of time elapsed)
Integrated rate laws: use the integrated rate laws to determine the value of k or concentration at
a given time
Applying Integrated Rate Law
•
•
In general, integrated rate law questions require you
to just implement the proper equation.
However, the order is essential to decide which
equation to use and it’s not always obvious. There
are some rules you should know:
–
–
Half lives: radioactive decay events are always first order;
decay events that are independent of concentration are
always second order
Graph axes: the axes on a graph can indicate the order of a
reaction
Integrated rate laws: use the integrated rate laws to determine the value of k or concentration at
a given time
Applying Integrated Rate Law: Straight
Line Form
•
The integrated rate laws can be written to yield
straight lines on the curves. The main difference
between them is the axes:
–
–
–
–
•
All graphs have time as the x axis
0th order: y-axis is concentration
1st order: y-axis is the natural log of the concentration
2nd order: y-axis is the inverse of the concentration
The other difference is the slope
–
–
0th and 1st order have a negative slope (slope = -k)
2nd order has a positive slope (slope = k)
Apply the rate law equations to graphs given information about the order of the reaction
Applying Integrated Rate Law: Radioactive
Decay
• Radioactive Decay is first order
• The equation above is extremely helpful because
the natural log term can be rewritten as a ratio,
instead of plugging in the actual concentrations.
– For example: if a question asks how long it takes for
a sample of Carbon – 14 to reach 1/1000 its original
amount (provided a value of k), you can substitute
the natural log term with 1000.
Integrated rate laws: use the integrated rate laws to determine solve problems using half-life
given information about the order
Summary
Factors Affecting Rates Learning Objectives
Understand that there are four main factors that affect rates
Understand how temperature affects the rate
Understand the main role and properties of a catalyst
Arrhenius law: Solve for new temperatures using a change in the
rate constant (k) or vice versa
• Apply Arrhenius law to graphs relating activation energy and
temperature to the rate constant
•
•
•
•
Four Factors that Affect the Rate and How
1.
Nature of reactants/ Availability of the molecules
•
•
2.
Larger surface area = faster rate
Ex: this is the reason why we chew our food (mechanical digestion)
Concentration
•
•
3.
Higher concentration, higher rate if your reaction is first order or
higher
Increases the rate based on the fact that the rate law is concentration
dependent
Temperature
•
•
4.
Higher temperature, higher rate always (in this class)
Increases the rate based on the fact that the rate constant in
temperature dependent
Catalysts
•
•
•
Catalysts decrease the activation energy, which increases the rate
The activation energy is decreased by modifying the substrate
orientation
Increases the rate based on the fact that the rate constant is
proportional to the negative activation energy
Understand that there are four main factors that affect rates
Arrhenius Theory
• Temperature can lead to a larger k value
– In this course, temperature always leads to a faster rate of reaction; when
wondering why, refer to the Boltzmann distribution
– A higher temperature increases the number of molecules with significant
energy to overcome the activation energy
Boltzmann
Distribution
Understand how temperature affects the rate
Arrhenius Law, Temperature
• The relationship between temperature and the rate
constant (k) is given by the formula:
• You can be asked to solve for a new k value or a new T
value.
• R = 8.314 J/mol x K ; Ea = activation energy (J); T =
Kelvin
• Things to remember about this formula:
– The order of k values is opposite the order of T values
– A higher T value gives a higher rate constant
– Distribute your terms!
Arrhenius law: Solve for new temperatures using a change in the rate constant (k) or vice versa
Arrhenius Law, Catalysis
• Arrhenius Law can be rewritten as a straight line slope,
but the equation isn’t immediately intuitive
– The intercept will always be lnA (A is the pre-exponential factor, NOT
CONCENTRATION)
– The slope will always be -Ea/R
• The role of a catalyst is to
lower the activation
energy
• Because the slope is
related to activation
energy, the presence of a
catalyst will make the
slope less negative
Apply Arrhenius law to graphs relating activation energy and temperature to the rate constant
Mechanisms Learning Objectives
• Use the elementary step of a reaction mechanism to determine the
rate law
• Apply the ideas of kinetic equilibrium to solve for the rate law of a
provided mechanism
• Identify the intermediates and reactants/products of a reaction
mechanism
• Identify the data associated with reaction coordinate diagrams
• Understand the attributes of transition state theory
Analyzing Steps of a Reaction Mechanism
• Consider the addition of chlorine to ethene:
•
•
•
If the first step is the slow step, what is the rate order?
• A mechanism is composed of multiple elementary steps
• The rate order is based on identifying if the elementary step is unimolecular or
bimolecular (the sum of coefficients of the elementary step reactants)
• This reaction mechanism can be written rate = k [HCl][C2H4]
Identify the intermediate(s)
• Intermediates are reagents that appear on both the product and reactant sides of
mechanism steps but cancel out of the overall balanced reaction
• The intermediates are CH3CH2+ and ClApply this mechanism to a reaction coordinate diagram…
Use the elementary step of a reaction mechanism to determine the rate law
Identify the intermediates and reactants/products of a reaction mechanism
Mechanisms: Reaction Coordinates
• Be able to identify/explain the following on a graph:
1. The number of steps
• The number of “humps” on a diagram; each representing a high energy transition state
2. The number of intermediates
• The number of valleys between humps
3. The transition states
• High energy, transient states
• Always represent a higher energy state than the previously existing
intermediate/reactant
4. Activation Energy of the reaction
• The energy difference between the reactant/intermediate and the transition state of the
rate-limiting step
5. Rate-limiting step (slow step vs. fast step)
• The hump with the greatest change in energy (not always the highest energy maxima
on the diagram)
6. The overall change in enthalpy
• The energy difference between the reactants and the products (think thermodynamic
state functions)
Understand the attributes of transition state theory
Identify the data associated with reaction coordinate diagrams
Mechanisms: Reaction Coordinates
• Consider the addition of chlorine to ethene:
Identify the following:
1. The number of steps
2. The number of
intermediates
3. The transition states
4. Activation Energy of the
reaction
5. Rate-limiting step (slow
step vs. fast step)
6. The overall change in
enthalpy
Observe the relationship
between the graph and the
proposed mechanism. Which
step in the mechanism is the
slow step?
Nuclear
Equilibrium and Mechanisms
•
•
When working with mechanisms, you write the rate law in terms of the
rate-limiting step.
However, you also want the rate law to be in terms of the actual reactants
(not the intermediates)
– When the rate-limiting step is not the first step of the proposed
mechanism, you have to do some additional work to find the rate law.
– What happens that enables us to do these problems is the fast steps that
come before the rate-limiting step reach equilibrium. This means the
forward rate is equal to the backwards rate.
Problems